(Adds Pelosi on progress, Senate blocks small business proposal, flight attendants urge airline aid)

By Susan Cornwell and David Morgan

WASHINGTON, Oct 20 (Reuters) - The White House and Democrats in the U.S. Congress moved closer to agreement on a new coronavirus relief package on Tuesday as President Donald Trump said he was willing to accept a large aid bill despite opposition from his own Republican Party.

With just two weeks to go until the U.S. presidential election, Trump signaled a willingness to go along with more than $2.2 trillion in new COVID-19 relief, as Democrats had been pushing for months.

"I want to do it even bigger than the Democrats," Trump said in an interview with Fox News, as talks between Pelosi, a Democrat, and Treasury Secretary Steven Mnuchin continued with the goal of getting something to pass Congress before Nov. 3.

Pelosi, speaking to reporters after a mid-afternoon call with Mnuchin, was asked about prospects for a legislative package by the end of this week.

"I hope so. That’s the plan," she said. She gave no details of her conversation.

Afterward, Pelosi Deputy Chief of Staff Drew Hammill said that a 45-minute call between the speaker and Mnuchin was productive "as they move closer to an agreement."

Hammill said negotiations will continue on Wednesday.

The White House has proposed $1.8 trillion in coronavirus relief, while Pelosi is pushing for $2.2 trillion.

Earlier on Tuesday, Pelosi told Bloomberg TV: "I'm optimistic, because I do think we have ... a shared value that finally they want to crush the virus. Hopefully by the end of the day today, we'll know where we all are."

Pelosi said aid to state and local governments and Republican demands for liability protection for businesses remain sticking points. But she suggested the Democrats could find grounds to agree on liability protections if the administration agrees to eliminate certain language sought by Republican Senate Majority Leader Mitch McConnell that she believes would overshadow protections for workers.

Senate Republicans have repeatedly stated their opposition to additional COVID-19 relief spending near the $2 trillion mark and have focused instead on smaller initiatives.

McConnell said that if Pelosi and the White House reach a deal and it's passed by the House, the Senate would consider it.

"I'm aware that discussions continue between the president and the speaker about a larger package," he told reporters. "Obviously, if that were to come over, we'd have to consider it. And would consider it."

However, several Senate Republicans were wary, non-committal or just plain negative about aid of $1.8 trillion or more.

"I think it's very unlikely that a number of that level would make it through the Senate, and I don't support something of that level," Senator Mitt Romney told reporters. "Something far more targeted to the people who really need help, I'd like to see done, and I'd like to see done as quick as possible."

FALL IN LINE

Trump predicted that Senate Republicans would fall in line if Mnuchin and Pelosi reach a broad bipartisan deal. He also said he would be willing to accept a deal passed mainly with Democratic support.

"Not every Republican agrees with me, but they will," he said. Trump added he specifically expects support from McConnell: "He'll be on board if something comes."

Pelosi and Mnuchin have been negotiating intermittently since August on a fresh plan to aid Americans slammed by the coronavirus pandemic, which has infected more than 8.2 million people, killed over 220,000 and thrown millions out of work.

Any new stimulus would be in addition to $3 trillion in relief that Congress approved earlier this year.

The head of the Association of Flight Attendants-CWA, Sara Nelson, sent a letter to members of Congress on Tuesday urging action before the election.

"Now is the time. There is no retroactivity that Congress can apply to the human toll caused by delayed relief," she said. More than 32,000 airline workers have been furloughed while awaiting another round of aid.

The Senate also plans a vote on Wednesday on a $500 billion-plus Republican proposal to include unemployment benefits and aid to schools. It would provide people with $300 in federal weekly unemployment benefits, while the Democrats want to return to the $600 weekly level in a measure approved earlier this year.

Democrats blocked a similar Republican proposal last month and the measure on Wednesday is also expected to fail. (Reporting by Susan Cornwell; additional reporting by Doina Chiacu and Susan Heavey; Editing by Scott Malone, Rosalba O'Brien, Bernadette Baum and Sonya Hepinstall)